I would say get rid of the employer ( start looking for other employers who are willing to do H1b transfer and file GC in near future). I am not sure why you decided to file h1b from such employer who didn't bear expenses for h1b filing. In the long run after you file GC, your employer might exploit you more with the fact that not all the people will change the employer when their GC is in the process. Is your employer a desi consultancy?
Just my 2 cents!